Question: Expand and combine like terms. $(9n^7-1)^2=$
Solution: We can expand this expression using the "perfect square" pattern (where $P$ and $Q$ can be any monomial): $(P+Q)^2=P^2+2PQ+Q^2$ Since we have a minus sign, let's rewrite the binomial as a sum where the second term is negative, then use the pattern. $\begin{aligned} &\phantom{=}\left(9n^7-1\right)^2 \\\\ &=\left(9n^7+\left(-1\right)\right)^2 \\\\ &=(9n^7)^2+2(9n^7)(-1)+(-1)^2 \\\\ &=81n^{14}-18n^7+1 \end{aligned}$